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Find the number of terms in each of the following A.P. (i) 7, 13, 19, …, 205 Q.5(1)

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Yesterday i was doing the question of arithmetic progressions of class 10th math of exercise 5.2. How i solve this question in easy way  Find the number of terms in each of the following A.P. (i) 7, 13, 19, …, 205

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  1. Therefore

    First term, a = 7

    Common difference, d = a2 − a1 = 13 − 7 = 6

    Let there are n terms in this A.P.

    an = 205

    As we know, for an A.P.,

    an = a + (n − 1) d

    Therefore, 205 = 7 + (− 1) 6

    198 = (n − 1) 6

    33 = (n − 1)

    n = 34

    Therefore, this given series has 34 terms in it.

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